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--- public:t-701-rem4:lab [2007/10/01 14:48] – created helgi
+++ public:t-701-rem4:lab [2024/04/29 13:33] (current) – external edit 127.0.0.1
@@ Line 1: / Line 1: @@
+See Myschool for original script (uncorrected)
+The following R code should be copied task by task (i.e. comment and code) and exectued in R. Its purpose is to show a simple prototype for an action, you should think about it, understand and try some variations.
+<code bash>
+# T-701-REM 4
+# 2007-10-01
+# Subjects from ch. 4.1, 4.3, 4.6 in ISwr.
+# limit "haed" data to men
+# suppose the workspace "haed.R" has been loaded
+men <- subset(haed, kyn=="karlar")
+str(men)
+attach(men)
+mean(cm)
+sd(cm)
+length(cm)
+# Do we need to change our established opinion (null hypothesis, "H0")
+# that average height of men is 180cm?
+t.test(cm, mu=180)
+# Computation of results element by element:
+# Standard error of the mean is the standard deviation of the sample distribution
+# of the mean (called SEM on pg. 82 in ISwR)
+# Assume here that the Central Limit Theorem can be used
+stderr <- sd(cm) / sqrt(length(cm))
+stderr
+# The value t is a measure of how far the sample is from the established opinion
+tvalue <- (mean(cm)-180) / stderr
+tvalue
+# Is this a big value in this context?
+# The p-value is the probabililty of a sample this far or further from H0 if H0 is correct
+# Low p-value (less than conf.level with a default value of 0.05)
+# indicates that H0 is wrong or we have a freak sample
+# Compute p-value corresponding to this t for df =38-1
+* (1-pt(tvalue, 37))
+# Confidence interval for the mean
+c( mean(cm)+qt(0.025, 37)*stderr, mean(cm)+qt(0.975, 37)*stderr)
+#
+# Try several variations of conf.level,
+# including 1-0.2659205 (Note: 1 minus the p-value, corrected 2007-10-06)
+# ############################
+# Compare heights of men and women (to see how t.test works)
+detach(men)
+rm(stderr, tvalue) # some cleanup (added 2007-10-06)
+attach(haed)
+# Test if the diff is 0 (reason for the name Null Hypothesis!)
+t.test(cm~kyn)
+# Conclusion?
+# Test if cm over 100 is a reasonable approximation to kg:
+t.test(kg, cm-100, paired=T)
+# Conclusion?
+######################################
+#
+# Another way of comparing group means (can be used with more than 2 grps)
+# ANOVA, ISwR, Ch. 6 (6.1 intro, 6.1.2, 6.5)
+# compute a linear model.
+# Use a categorical explanatory variable:
+lm(cm~kyn)
+summary (lm(cm~kyn))
+anova(lm(cm~kyn))
+# Compare "Mean Sq" of "Residuals" with
+var(cm)
+# Compare total of "Sum Sq" column formula on middle of pg. 112 and with
+sum((cm-mean(cm))^2)
+var(cm)*51
+# Conclusion?
+######################################
+#
+# The classical "best line" is a linear model too:
+lm (kg~cm)
+summary(lm(kg~cm))
+anova(lm(kg~cm))
+# One reason for the limited standard output of lm:
+plot(cm, kg)
+abline(lm(kg~cm))
+# Exercise:
+# Try to find out if the point (mean(cm), mean(kg)) lies on the line
+</code>